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This photo of Comet C/2014 Q2 Lovejoy was taken in late December 2014 at an approximate magnitude of 5.6. Photo courtesy Wikimedia, photo by Paul Stewart.

Earthlings had their last chance for 8,000 years to see Comet Lovejoy Saturday night.

The opportunity to look up and see its green glow came when the comet was six days away from perihelion. On Jan. 30 the comet, formally known as Comet C/2014 Q2 Lovejoy, will be 193 million kilometers from the sun.

The comet actually passed closest to Earth on Jan. 7, when it was 70.2 million kilometers away.

It will be about 13,000 years before Comet Lovejoy is again close enough to Earth to be seen without the aid of a magnifying device.

How do scientists know how long it has been since a comet was visible with only the eyes from the surface of our planet?

The answer involves mathematics. Among the laws of planetary motion discovered by Johannes Kepler is the equation necessary to determine a comet’s period, or the amount of time needed to complete an orbit, if its semi-major axis is known. The semi-major axis of an ellipse, which is the shape that most objects in orbit around the sun follow, is best thought of as the radius of the ellipse at its two points that are most distant from each other.

This graphic shows the semi-major and semi-minor axes of an ellipse. Courtesy Wikimedia.

Kepler determined that the square of the ellipse’s period is equal to the cube of the semi-major axis’ length.

Another interesting feature of Comet Lovejoy’s orbit is its orientation relative to the plane of Earth’s and the other planets’ orbits. As Phil Plait explained at Bad Astronomy, the comet sits about 80 degrees off those trajectories.

Nearly three years of quiet from a probe speeding toward a rendezvous with a distant comet ended Monday as engineers in Germany successfully reactivated the Rosetta spacecraft.

The solar-powered probe is designed to be the first to land on a comet. If all goes as planned, Rosetta will accomplish that feat in November of this year when an onboard lander alights on the head of comet 67P/Churyumov-Gerasimenko.

Rosetta will also follow the comet around the sun, another first for human space exploration.

The probe’s reactivation came at 18:18 Greenwich Mean Time (11:18 MST). The Twitter account set up for Rosetta announced it a few minutes later with a cheery “Hello, World!”

Rosetta was launched on March 2, 2004. During the 118 months that have since elapsed it has flown by the Earth three times and once around Mars. The probe was placed into hibernation at the command of engineers in Europe on June 8, 2011.

During the hibernation only the computers onboard and heaters necessary to prevent the spacecraft from freezing were functional. All other instrumentation, including that necessary to study the comet, was shut down.

The deactivation of Rosetta was necessary because the probe would travel too far from the Sun to obtain the solar energy needed to power its systems.

Reactivation occurred when a timer programmed into the spacecraft’s computer system reached the previously specified time of the event. Rosetta’s star trackers were the first instruments to come back online. Then the probe’s computer system slowed the spacecraft’s spin and oriented it toward Earth in order to transmit a signal.

“This was one alarm clock not to hit snooze on, and after a tense day we are absolutely delighted to have our spacecraft awake and back online,” Fred Jansen, the European Space Agency’s manager for the mission, said in a statement.

Now about nine million kilometers from comet 67P/Churyumov-Gerasimenko, Rosetta will enter an orbit around the comet in May.

In November, after Rosetta has had time to slow down enough time to synchronize its velocity with the comet, a smaller craft called Philae will land on it.

Philae, which has a mass of about 100 kilograms, is much smaller than the nucleus of the comet.

“The comet itself, it’s about four kilometers across,” Michael R. Combi, a professor in the University of Michigan’s Department of Atmospheric, Oceanic, and Space Sciences and a member of the Rosetta scientific research team, said. “The lander is very small. I don’t think it’s two feet across.”

Philae will contend with landing on a surface that exhibits very little gravity. Unlike Earth, where there is enough gravity to hold soil and rock in place, the environment on a small comet like 67P/Churymov-Gerasimenko does not have enough to hold all solid material in place.

“It’s fairly fluffy,” Combi said. “There’s almost no gravity at the surface of an object that small.”

The comet has about 1,000 times less gravity than does Earth.

The lander will study 67P/Churyumov-Gerasimenko’s nucleus, and determine the chemical composition of the materials found there, while being secured to the comet’s nucleus by two harpoons.

“We want to measure all we can, how much material is coming off the comet as it goes around the sun,” Combi said.

He explained that ice is the dominant material on a comet’s nucleus, and that it sublimates, or changes phase from a solid to a gas, as the comet heats up on approach to the sun. One of the mission’s goals is to understand the mechanics of this sublimation process.

Rosetta also aims to help scientists gain a better understanding of the specific chemical makeup of comets.

“Practically all seem to be dominated by water ice,” Combi said. “Then there’s this rocky, dusty material and some organic material. There’s a whole host of other volatiles – carbon dioxide, carbon monoxide, methanol. Most comets seem to have those materials in them, but the ratios do vary.”

One unique feature of the mission will be to allow the measurement of carbon dioxide in the nucleus, a task that is not possible from Earth.

“It’s very difficult to observe some of the chemical species when they’re far away and faint,” Combi said in a statement. “Carbon dioxide is probably the second most abundant species at most comets, but it’s not been observed in the thousands we’ve looked at from Earth.”

Another priority will be to study the solar wind, which can produce solar storms.

Composed of a stream of charged particles, the solar wind exhibits different velocities at different locations on the sun. Since Earth’s orbit takes it closest to the equator of the sun, it is difficult for scientists to study the dynamics of the solar wind at higher solar latitudes.

“But comets pass through all of it. With their help, we can study the fast solar wind,” Tomas Gombosi, a professor of engineering in UM’s Department of Atmospheric, Oceanic, and Space Sciences and another researcher on the Rosetta team, said in a statement.

Of course, as relics from the earliest days of the solar system, Rosetta should also provide significant insights about the distant past of our stellar neighborhood.

“Comets, more than most other objects in the solar system, preserve information about the solar system when it was formed,” Gombi explained.

The Rosetta mission was designed to replace a similar undertaking conceived by NASA called the Comet Rendezvous Asteroid Flyby during the 1980s. That proposed mission would have involved flying a probe alongside a comet for three years. It was cancelled in 1992 as a result of budget constraints facing the American space agency at that time.

The Rosetta mission will end in 2015 after completing the orbit of the sun alongside comet 67P/Churyumov-Gerasimenko.

The Rosetta spacecraft will come closest to the sun on Aug. 13, 2015, when it and the comet are about 185 million kilometers away from our star.